Realize that the Metro has its own risks. Pick-pocketing is a moderate danger here so be aware of your surroundings, and keep an eye on your belongings. Especially, don't take the Metro during rush hour unless you are especially fond of the sensation a sardine has in a tin.

How bad is the metro really? I would carry one largish backpack, and head to the centre between 6-7 o'clock in the morning. I can usually adapt to different surroundings easily and I speak Spanish.

Would it actually be likely that someone tries to steal my stuff, seeing I'm fresh out the airport? Should I play it safe and take the metrobus or maybe a taxi instead?

Besides security, are there other good reasons to prefer metrobus or taxi? (Looking at the metro map, I'd have to change lines at least once.)

If you don't already know Mexico City I would take an airport taxi from the airport the first time - they're regulated.
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hippietrailFeb 8 '13 at 14:54

In my experience Mexico City is a place where you can try to look confident or tough and it will discourage people from messing with you. In other places this will attract more dodgy attention. Still I knew a large muscly American guy who got pickpocketed or robbed on the Mexico City subway.
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hippietrailFeb 12 '13 at 3:42

2 Answers
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Don't know of a single person that's had a problem on the subway/metro. You grab it from Terminal 1, it's around 3 pesos. Almost everyone that works at the airport takes this bus into the city. Foreign travelers forget that not everyone that goes to the airport takes a limo.

Some people like the #4 metrobus because it has security surveillance and usually an officer on board, it's 10x more expensive then the metro however (although 30 pesos isn't a bank breaking increase). You'll like not see a single local on this bus.

Taxis are fine just make sure that you get an official one from the stand and not a scooper. I hate that as a foreigner (and almost only foreigners take taxis from the airport), you'll be hard pressed to get a rate under 200 pesos into the city, and usually there's some sort of scam attached.

Since you're travelling during morning rush hour, sound like you're packing light and sound well researched I probably wouldn't hesitate to take the subway. Although if you're still nervous about it, 27 pesos for piece of mind sounds like a worthwhile expense. Best of Luck!

Believe me, you have better odds of being safe in the Metro than taking a taxi/metrobus and it will be faster & cheaper than any of the other options.
You can get around by taking one of the regulated taxis as @hippietrail suggests, however in Mexico City you HAVE to take the metro at some point, so there's pretty much two options: take it now or take it later, but whether you think it's insecure that's another matter.
Report of theft in the metro is actually the same as any big city and pickpocketing is actually lower than in some parts of Europe such as in Paris, the Wikipedia article for Mexico city even lists a non-referenced paragraph that states that Mexico City is actually safer that Washington DC & Moscow.
To add some stats to the above comments, here is a chart (in spanish) from 2010-2011 about the number of thefts per transportation system:

As you can see, the metro is actually the lowest and even when the theft to vehicles (asalto a vehiculos) is pretty high, the article states 1 every 300,000 vehicles gets mugged. As for the metro, the same article states that "Matemáticamente, la probabilidad de ser asaltado en el metro cada día es 1 en 15 millones.", meaning, the odds of getting mugged in the metro is 1 every 15 million. It would seriously be a lot of bad luck if something happens to you in the metro.

Being the above being said and comparing to the warning issued by the US Travel Gov site to say, similar large metro networks such as France's: France crime; you can guess that Mexico City is like any other major city in the world where you have some odds of getting mugged or pickpocketed specially if you do not look from around and you find yourself stopping & staring at a map on every corner.

I am not exactly sure where you are heading to, since the Metro in downtown Mexico City involves quite a lot of metro stations, but here is a map of the most recurrent thefts in Mexico City by location, issued by one of the largest newspapers in the country (keep in mind that although the map looks kinda crowded, you are looking at a 21.2 million people city according to Wikipedia):
El Universal / Google Maps - Mapa delictivo del DF

My last advice is that Mexico City is quite a wonderful city to visit too, and although I won't lie - there are some chances of you getting mugged or pickpocketed, the odds for you having a very pleasant trip are a lot higher, specially if you speak spanish.

Take precautions as in any other big city you would be travelling into: beware of really crowded metro stations (if you are not in a hurry just wait for the next wagon), keep ipods/cameras/cellphones hidden, have copy of your passport / most important documents attached to your body and you should have an awesome time in Mexico.

I still wouldn't recommend newcomers who've never been on the DF Metro before to jump straight on with all their luggage and lack of sleep after their flight. Even though that's what I do (-; There's plenty of time to ease into the Metro when you don't have tons of luggage. I never see locals with luggage using the Metro for the airport either. Though I've never been pickpocketed on the Metro I've been with groups of friends when one or more of them were, or had bags or pockets slashed, and I caught somebodies fingers trying to get in my pocket once.
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hippietrailFeb 12 '13 at 1:09

@hippietrail I understand your point about taking all their luggage, yet he says he is travelling only with one large backpack to which he can accommodate fairly easy in the metro. Also nowhere in the question above I see a point of lack of sleep and overall he's asking how bad the metro really is? I just provided stats for that and overall suggestions. Also as a former local of the city - I saw heaps of people taking the metro with luggage both foreign and local.
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Osvaldo M.Feb 12 '13 at 3:30

Keep in mind that Stack Exchange is not intended primarily for one-on-one answers but to be a repository of answers that will be helpful to many people, most of whom will arrive at the sites via search engines. So while this particular OP might have just one backpack, not everbody who finds this topic while looking for advice will be in the same situation. We shouldn't assume all readers will have small amounts of luggage or short flights. We should assume many varied people wanting to know how to get from Mexico City aiport to downtown will come here.
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hippietrailFeb 12 '13 at 3:34

The stats were great by the way! I only downvoted because I'm worried naive people could take this advice and run into problems. Personally I would've assumed Moscow and DC would be more dodgy than DF too. I definitely see loads more people on the metro to/from the airport in places like France, Germany, Turkey, Japan, Korea, Sydney though.
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hippietrailFeb 12 '13 at 3:38